Question 1000183
{{{y=x^2}}} as the start.


Expanded vertically by factor 4 would be  {{{y=4x^2}}}, but HORIZONTALLY should be {{{4y=x^2}}}.


Reflect accross the y-axis would be no real change.  y-axis is the axis of symmetry for this up to now.  


Move 3 unit leftward:  {{{4y=(x-(-3))^2}}}.


Move 5 unit upward:  {{{4(y-5)=(x-(-3))^2}}}.


Simplify and you are probably wanting to finish in standard form, so these steps...

{{{4(y-5)=(x+3)^2}}}
{{{y-5=(1/4)(x+3)^2}}}
{{{highlight(y=(1/4)(x+3)^2+5)}}}




If you called your original function f(x), then you could call you changed function something else, like g(x).